A Genuine Question In Mathematical Philosophy

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Alan Masterman
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A Genuine Question In Mathematical Philosophy

Post by Alan Masterman » February 15th, 2018, 7:31 am

I offer the following question.

(1) Mainstream mathematics assures us there are several proofs to show that 0.999... = 1.

(2) Peano Arithmetic and Set Theory (as conjoined and exemplified, for example, in Cantor's Diagonal Argument) tell us that 0.999... is the largest real number which is less than 1.

(3) If 0.999... = 1, it would appear that parallel lines, and lines which intersect at infinity, are mathematically indistinguishable, with significant consequences for Euclidean geometry.

May I solicit your comments?

Namelesss
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Re: A Genuine Question In Mathematical Philosophy

Post by Namelesss » February 19th, 2018, 8:49 pm

Alan Masterman wrote:
February 15th, 2018, 7:31 am
On the off-chance that this is still a serious philosophy forum, and hasn't been totally hijacked by Growthhormone and those silly enough to dignify his or her posts with a reply, I offer the following question.
This has been reported. Keep your personal problems... personal!
Violation the ToS.
0.999... = 1.
Is absurd!
Ultimately, it is no more than a desperate attempt by 'believers' to justify the obsolete belief in materialism/physicalism. It is meaningless, emotional, crap.
That also means that the notion/definition of a tangent must be dismissed as an impossibility.
It is pathetic.

Chili
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Re: A Genuine Question In Mathematical Philosophy

Post by Chili » February 20th, 2018, 12:52 am

.999 approaches 1 as you add nines

Steve3007
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Re: A Genuine Question In Mathematical Philosophy

Post by Steve3007 » February 20th, 2018, 6:59 am

Alan Masterman wrote:...those silly enough to dignify his or her posts with a reply
I think I may have replied to Growthhormone, but fortunately my posts aren't capable of dignifying anything.
Alan Masterman wrote:Mainstream mathematics assures us there are several proofs to show that 0.999... = 1.
I assume you mean an infinite number of 9's. I would have thought that mathematics says something more like "0.999... tends towards 1 as the number of 9's increases", which is a different thing. By increasing the number of 9's you can get arbitrarily close to 1, which means that for any given number of 9's it's always possible to add another.
Namelesss wrote:Ultimately, it is no more than a desperate attempt by 'believers' to justify the obsolete belief in materialism/physicalism. It is meaningless, emotional, crap...
I've never known anybody to get angry about sums before. Great stuff.
Chili wrote:.999 approaches 1 as you add nines
Yes. Sounds reasonable.

Namelesss
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Re: A Genuine Question In Mathematical Philosophy

Post by Namelesss » February 20th, 2018, 8:05 am

Steve3007 wrote:
February 20th, 2018, 6:59 am
Namelesss wrote:Ultimately, it is no more than a desperate attempt by 'believers' to justify the obsolete belief in materialism/physicalism. It is meaningless, emotional, crap...
I've never known anybody to get angry about sums before. Great stuff.
Glad you can appreciate it. *__-
The emotion is because people identifying with their beliefs; materialism, in this case.
When a 'belief' feels threatened, so does the person.
That is why emotion, at some level, rather than rational/logical thought becomes involved...

Or, you've never seen, or been, someone working hard at the old blackboard and, at some point, feels frustration? Frustration is the feeling, anger the expression (or one expression).
(Throws chalk across room over sums!)

Steve3007
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Re: A Genuine Question In Mathematical Philosophy

Post by Steve3007 » February 20th, 2018, 8:25 am

OK. But I would hope you're at least aware of the absurdity of saying that the statement:

"0.999... = 1"

is

"no more than a desperate attempt by 'believers' to justify the obsolete belief in materialism/physicalism. It is meaningless, emotional, crap."

It's just somebody making a proposition about the nature of infinitesimals and limits.

Namelesss
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Re: A Genuine Question In Mathematical Philosophy

Post by Namelesss » February 21st, 2018, 1:19 am

Steve3007 wrote:
February 20th, 2018, 8:25 am
OK. But I would hope you're at least aware of the absurdity of saying that the statement:

"0.999... = 1"

is

"no more than a desperate attempt by 'believers' to justify the obsolete belief in materialism/physicalism. It is meaningless, emotional, crap."

It's just somebody making a proposition about the nature of infinitesimals and limits.
And now we have two Perspectives.
Go play with someone else.

Steve3007
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Re: A Genuine Question In Mathematical Philosophy

Post by Steve3007 » February 21st, 2018, 5:19 am

To Alan Masterman:
Namelesss wrote:This has been reported. Keep your personal problems... personal!
Violation the ToS.
Namelesss, can you see the irony/hypocrisy in your saying this, given that so many of your own posts contain derisory, ad hominem, snarky or sarcastic comments against the people who are trying to talk with you?
Namelesss wrote:It is meaningless, emotional, crap.
Namelesss wrote:Then feel free to STFU and listen.
(STFU is an acronym for "Shut the f**k up".)
Namelesss wrote:Go play with someone else.
etc.

If you treat others with a little respect, and don't simply dismiss them with expletives, you may get some respect in return. If you don't, you probably won't. If a subject as innocuous as mathematics causes an emotional reaction in you, then, as you yourself have said to the original poster in this topic, this is your personal problem. Perhaps you should keep it to yourself?

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mathman
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Re: A Genuine Question In Mathematical Philosophy

Post by mathman » March 2nd, 2018, 11:11 pm

I think what he meant was 0.999 APPROACHES 1. 0.9999 would be larger to 1 than the former. So keep adding 9's would not reach "1" ever because the number would in fact become smaller each time required to get to "1" but it tends to 1 in the mathematical sense as the first significant figure after the decimal ruled it out of ever becoming a "1".

Steve3007
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Re: A Genuine Question In Mathematical Philosophy

Post by Steve3007 » March 6th, 2018, 7:04 am

One way to express it is to use the language of the Theory of Limits and say that 1 is the limiting value of 0.999 as the number of decimal places tends towards infinity. This is different from simply saying "0.999... = 1".

http://people.sju.edu/~pklingsb/limitthy.pdf

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Atreyu
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Re: A Genuine Question In Mathematical Philosophy

Post by Atreyu » March 13th, 2018, 6:18 pm

I remember than in my high school geometry class our teacher taught us that .9999.... = 1

One way he proved it was by multiplying each side of the equation '.3333...= 1/3' by 3.

Right?

Erribert
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Re: A Genuine Question In Mathematical Philosophy

Post by Erribert » May 1st, 2018, 12:15 am

I am glad you are asking about mathematical philosophy rather than mathematics. In mathematical philosophy, the philosophical concept of infinity can exist. Infinity does not exist in mathematics because it is purely conceptual and has no value. This is similar to eternity not being a unit of time.

Unfortunately, modern physics since the turn of the century has mistakenly confused infinity as a mathematical quantity. Einstein’s general theory of relativity is derived from this type of mathemagics. Steven Hawking would speak of “near infinite temperatures” when explaining the Big Bang. So, how close to infinity does one have to get to be “near” it? Would this be infinity minus 100, 1,000, 1 billion degrees? Just plain silly in my opinion.

Most theoretical math in physics these days is mathematical philosophy rather than mathematics. Mathematics is for making testable predictions, not for philosophizing about black holes that nobody can create experiments around (and no Bose-Einstein condensates, please). Black holes fall within the discipline of mathemagics. It’s how clever physicists or theoretical mathematicians fool the general public and “find” Higgs Bosons for a mere $15B!

So, according to mathematical philosophy, or metaphysics, YES, your infinite 0.9999... equals exactly one. However, I would not try to cheat the stock market with such mathematical trickery.

Cheers

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Jacqueline Sheehan
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Re: A Genuine Question In Mathematical Philosophy

Post by Jacqueline Sheehan » May 8th, 2018, 2:57 pm

https://en.wikipedia.org/wiki/0.999...
There are many ways to prove that 0.999... = 1,
Infinite -series, algebra arguments, etc.

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Halc
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Re: A Genuine Question In Mathematical Philosophy

Post by Halc » May 11th, 2018, 8:01 am

Alan Masterman wrote:
February 15th, 2018, 7:31 am
(1) Mainstream mathematics assures us there are several proofs to show that 0.999... = 1.
Unclear how genuine your interest is in any of this. You've not posted a single response since opening this topic.

From what I've read by those that are more experts in this subject than I, this issue was unresolved for some time, and certain fundamental axioms had to be assumed for them to say these were equal. If different axioms are assumed, they are not equal. But mainstream mathematics runs under the former axioms. The other axioms are not wrong because of this. They're just not as mainstream.
(2) Peano Arithmetic and Set Theory (as conjoined and exemplified, for example, in Cantor's Diagonal Argument) tell us that 0.999... is the largest real number which is less than 1.
This seems contradictory, but maybe I'm wrong. This seems to imply that .999... is unequal to 1, but the average between these two unequal numbers does not lie between them, or if it does, then .999... is not the largest real number less than 1. How is that not a contradiction?
(3) If 0.999... = 1, it would appear that parallel lines, and lines which intersect at infinity, are mathematically indistinguishable, with significant consequences for Euclidean geometry.
What would these consequences be? Indistinguishable doesn't mean there is actually a point of intersection since infinity isn't a specific number, else they'd cross there and grow apart at points beyond infinity.


A few random comments:
mathman wrote:
March 2nd, 2018, 11:11 pm
So keep adding 9's would not reach "1" ever because the number would in fact become smaller each time required to get to "1" but it tends to 1 in the mathematical sense as the first significant figure after the decimal ruled it out of ever becoming a "1".
Chili wrote:
February 20th, 2018, 12:52 am
.999 approaches 1 as you add nines
True, but .999... is not the same as a series with a limit. It is a number with no more 9's to 'keep adding', and numbers don't approach anything.
Atreyu wrote:
March 13th, 2018, 6:18 pm
I remember than in my high school geometry class our teacher taught us that .9999.... = 1

One way he proved it was by multiplying each side of the equation '.3333...= 1/3' by 3.

Right?
This is begging and thus an invalid proof. If 0.999... is not equal to 1, then 0.333... is not equal to 1/3. So one must assume the conclusion to prove the conclusion.

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